Sankhya: The Indian Journal of Statistics

1998, Volume 60, Series A, Pt. 1 ,pp. 74-89

BAYES ESTIMATION OF DIRICHLET PROCESS PARAMETER

By

JOSE G. LEITE,
* University of S\=ao Paulo, S\=ao Paulo*

VICTOR H. SALINAS-TORRES,*University of Santiago, Santiago*

RAM C. TIWARI,*University of North Carolina, Charlotte*

and

JYOTI N. ZALKIKAR ,*Florida International University, Miami*

*SUMMARY.* Dirichlet process serves as a prior for the unknown distribution function in
nonparametric Bayes estimation of various parameters. The present article
addresses the problem of finding Bayes estimator of Dirichlet process
parameter itself, with respect to the discrete prior distribution
concentrating on finite number of fixed points. This problem is related to
the estimation of the parameter of independent and non-identically
distributed Bernoulli model. We show that in the limiting case as the sample
size increases to infinity, the Bayes estimator converges to the prior
supported point ``closest'' to the ``true'' parameter value, which may not
be a prior-supported point. This result exemplifies a typical Bayesian
phenomenon that the posterior distribution is dominated by the prior
distribution.

*AMS (1991) subject classification.* Primary 62G05; secondary 62C10, 60G99.

*Key words and phrases. *Jensen's inequality, prior sample size, maximum
likelihood estimator.